quantum algorithms:
Topological Physics – Phenomena in physics controlled by the topology (often: the homotopy theory) of the physical system.
General theory:
In metamaterials:
For quantum computation:
The anomalous Hall effect is like a Hall effect but in the absence of a (substantial) external magnetic field, whose role is instead played by Berry curvature of the band, non-vanishing over the Brillouin torus of Bloch momenta, such as may be caused by intrinsic magnetization or strong spin-orbit coupling in the given crystalline material:
Like the ordinary Hall effect is caused by the Lorentz force which is exerted on electrons moving in “real” space filled with a magnetic flux density , so the anomalous Hall effect is caused analogously by an “anomalous velocity” contribution due to the Berry curvature in momentum space.
Historically, the microscopic understanding of the anomalous Hall effect had been slow and was riddled by debates. In modern understanding it is primarily due to non-vanishing Berry curvature over the Brillouin torus of the crystalline material, which plays the role of magnetic flux density in “reciprocal” momentum-space (cf. Sinitsyn 2008, Nagaosa et al 2010).
As such, the anomalous Hall effect is a “quantum” effect on par with the quantum Hall effect, and indeed the two combine in quantum anomalous Hall systems.
Types of Hall effects
The original observation:
Review with emphasis on the explanation of anomalous velocity via Berry curvature:
Di Xiao, Junren Shi, Qian Niu: Berry phase correction to electron density of states in solids, Phys. Rev. Lett. 95 (2005) 137204 [arXiv:cond-mat/0502340, doi:10.1103/PhysRevLett.95.137204]
Nikolai A. Sinitsyn: Semiclassical theories of the anomalous Hall effect, Journal of Physics: Condensed Matter 20 2 (2008) [arXiv:0712.0183, doi:10.1088/0953-8984/20/02/023201]
Naoto Nagaosa, Jairo Sinova, Shigeki Onoda, Allan H. MacDonald, N. P. Ong: Anomalous Hall effect, Rev. Mod. Phys. 82 (2010) 1539 [arXiv:0904.4154, doi:10.1103/RevModPhys.82.1539]
Di Xiao, Ming-Che Chang, Qian Niu, section III.D of: Berry phase effects on electronic properties, Rev. Mod. Phys. 82 (2010) 1959 [arXiv:10.1103/RevModPhys.82.1959]
See also:
Last revised on June 2, 2025 at 11:26:30. See the history of this page for a list of all contributions to it.